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Welcome to OTIlib and pyoti documentation!
==============================================
The OTIlib and pyoti library is a C and Python library to support the Order Truncated Imaginary (OTI) algebra. OTI numbers were developed in the Ph.D. thesis "Order Truncated Imaginary Algebra for Computation of Multivariable High-Order Derivatives in Finite Element Analysis" (`link `_). OTI numbers are an extension of Dual numbers. Dual numbers are a hypercomplex algebra that allows computing a single first order derivative per evaluation. OITs, is also a hypercomplex algebra, but in contrast to dual numbers, it can be used to compute efficient high-order derivatives with respect to multiple variables. In contrast to the Dual numbers ( :math:`a + b \epsilon, \epsilon^2 = 0` ), OTI numbers set a truncation condition other than :math:`\epsilon^2 = 0`, and considers multiple imaginary basis. For instance :math:`\epsilon_1^5, \epsilon_1^2\epsilon_2, \ldots, \epsilon_m` can be non-truncated imaginary directions.
More information on HYPAD
=========================
* Theory, references, lecture notes and other information on Hypercomplex-based Automatic Differentiation `HYPAD `_.
.. warning::
This website is under construction. Documentation placed here may be incomplete.
Development is constantly being done to improve documentation.
Quick example:
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.. literalinclude:: ../../examples/python/quick_example.py
:language: python
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Contents
========
.. toctree::
:maxdepth: 2
:caption: Contents:
installation
tutorials
examples
aboutus
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Module documentation
====================
.. toctree::
:maxdepth: 1
:caption: Module documentation:
pyoti
Indices and tables
==================
* :ref:`genindex`
* :ref:`modindex`
* :ref:`search`